Question

There is a hemispherical bowl. A cone is to be made such that, if it is filled with water twice and the water is poured in the bowl, it will be filled just completely. State how will you decide the radius and perpendicular height of the cone.

Answer 1

Volume of hemisphere = 2/3 πR³

Volume of cone = 1/3 πr² × h

By the given condition ; 

2 × volume of cone = volume of hemisphere

∴ 2 × 1 / 3 πr² h = 2/3 πR³ 

∴r² h = R³ 

∴ if r = h = R .......then both sides will be equal. 

∴ if radius of base of the cone is R and its height is R, which is equal to radius of the bowl, then a cone satisfying the given condition can be made.